Two-Timescale Stochastic Approximation for Bilevel Optimisation Problems in Continuous-Time Models

TL;DR

This paper analyzes a continuous-time, two-timescale stochastic approximation algorithm for bilevel optimization, establishing its convergence properties and demonstrating its applicability to various continuous-time problems.

Contribution

It provides the first weak convergence rate analysis of a continuous-time two-timescale stochastic approximation algorithm for bilevel optimization.

Findings

Established a central limit theorem for the algorithm's convergence

Demonstrated the algorithm's application to multiple continuous-time bilevel problems

Provided insights into the asymptotic behavior of the algorithm

Abstract

We analyse the asymptotic properties of a continuous-time, two-timescale stochastic approximation algorithm designed for stochastic bilevel optimisation problems in continuous-time models. We obtain the weak convergence rate of this algorithm in the form of a central limit theorem. We also demonstrate how this algorithm can be applied to several continuous-time bilevel optimisation problems.